Comparison of apodizing properties of glass stops with different transmission functions

A comparison of the apodizing properties of glass stops with different forms of the transmission function are used to derive general relationships governing apodization of laser beams. The dependences of the maximum attainable degree of apodization on the minimum transmission of a stop at the edge, and of the apodization length on the relative width of the variable transmission zone are derived. The quality of apodization of laser radiation by stops is compared allowing for the filling factor and for the phase inhomogeneity acquired during the manufacture of the stops.